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Canadian Journal of Physics

Quantum quench and time evolution of mutual information with hyperscaling violation

Zahra Zarrin, Mohammad Reza Tanhayi

Published Oct 18, 2022• 0 citations
Publisher

Abstract

We studied the time evolution of the mutual information after a quantum quench in the strongly coupled field theories. We use a hyperscaling-violating background and generalize the results of Tanhayi (JHEP, 1603, 202 (2016). doi: 10.1007/JHEP03(2016)202) to subregions with unequal lengths. Precisely, we consider two different strips as the entangling regions and use a holographic prescription to obtain the corresponding mutual information due to a time-dependent coupling in the probe sector. In this setup, due to the formation of apparent horizons, the thermalization can happen and we show that in this process the mutual information remains positive; nevertheless, for three entangling regions the corresponding quantity is negative.

DOI
10.1139/cjp-2020-0350

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We studied the time evolution of the mutual information after a quantum quench in the strongly coupled field theories. We use a hyperscaling-violating background and generalize the results of Tanhayi (JHEP, 1603, 202 (2016). doi: 10.1007/JHEP03(2016)202) to subregions with unequal lengths. Precisely, we consider two different strips as the entangling regions and use a holographic prescription to obtain the corresponding mutual information due to a time-dependent coupling in the probe sector. In this setup, due to the formation of apparent horizons, the thermalization can happen and we show that in this process the mutual information remains positive; nevertheless, for three entangling regions the corresponding quantity is negative.
We study certain features of scaling behaviors of the mutual information during a process of thermalization, more precisely we extend the time scaling behavior of mutual information which has been discussed in [1] to time-dependent hyperscaling violating geometries. We use the holographic description of entanglement entropy for two disjoint system consisting of two parallel strips whose widths are much larger than the separation between them. We show that during the thermalization process, the dynamical exponent plays a crucial rule in reading the general time scaling behavior of mutual information (e.g., at the pre-local-equilibration regime). It is shown that the scaling violating parameter can be employed to define an effective dimension.
We study the time evolution of holographic mutual and tripartite information for a zero temperature CFT, derives to a non-relativistic thermal Lifshitz field theory by a quantum quench. We observe that the symmetry breaking does not play any role in the phase space, phase of parameters of sub-systems, and the length of disentangling transition. Nevertheless, mutual and tripartite information indeed depend on the rate of symmetry breaking. We also find that for large enough values of δt the quantity teqδt−1, where δt and teq are injection time and equilibration time respectively, behaves adiabatically, i.e. its value is independent of length of separation between sub-systems. We also show that tripartite information is always non-positive during the process indicates that mutual information is monogamous.
This thesis collects three works about holographic computations of entanglement entropy. In the first one it is shown how to compute numerically, following the Ryu-Takayanagi prescription, the entanglement entropy for arbitrarily shaped entangling regions in three dimensional conformal field theories. The other two focus on holographic theories with hyperscaling violating exponents: the time dependence after a holographic quench is analyzed and the arising of new universal terms due to the presence of non smooth boundaries is shown.
The mutual and tripartite information between pairs and triples of disjoint regions in a quantum field theory are sensitive probes of the spread of correlations in an equilibrating system. We compute these quantities in strongly coupled two-dimensional conformal field theories with a gravity dual following the homogenous deposition of energy. The injected energy is modeled in anti-de Sitter space as an infalling shell, and the information shared by disjoint intervals is computed in terms of geodesic lengths in this background. For given widths and separation of the intervals, the mutual information typically starts at its vacuum value, then increases in time to reach a maximum, and then declines to the value at thermal equilibrium. A simple causality argument qualitatively explains this behavior. The tripartite information is generically nonzero and time-dependent throughout the process. This contrasts with (but does not contradict) the time-independent tripartite information one finds after a two-dimensional quantum quench in the limit of large time and distance scales compared to the initial inverse mass gap.
We examine the holographic entanglement entropy in hyperscaling violating backgrounds. Precisely in such theories, by semianalytic computation, we use holographic methods to derive the universal terms of entanglement entropy in various dimensions. We also find such terms when the bulk action includes higher-order curvature terms. We make further comments on the mutual information in hyperscaling violating backgrounds with higher curvature interactions. We explore the sign of tripartite information, which results in a monogamy property on mutual information. It is shown that for various hyperscaling parameters, the mutual and tripartite information are always positive and negative, respectively. This indicates that mutual information is monogamous in theories with hyperscaling violation.
We study various quantum quench processes induced by the Möbius/sine-square deformation of the Hamiltonian in two-dimensional conformal field theories starting from the thermofield double state in the two copies of the Hilbert space. These quantum quenches, some of which are directly related to the operator entanglement of the time-evolution operators, allow us to study scrambling and recovery of quantum information. In particular, under the sine-square deformed time evolution, we show from the time dependence of mutual information that the Bell pairs, initially shared by the subsystems of the two Hilbert spaces, may revive even after the mutual information for small subsystems is completely destroyed by quantum information scrambling dynamics. This mutual information is robust against the strong scrambling dynamics. As a consequence, the steady state has a nonlocal correlation shared not by any of two parties but by three parties. In the holographic dual description, a wormhole connecting the two Hilbert spaces may nonlinearly grow with time during the quantum quenches. We also propose effective pictures that describe the dynamics of mutual information during the time evolution by inhomogeneous Hamiltonians. Published by the American Physical Society 2024